Show that if is any multiplicative closed subset of where is commutative ring with unity,

Apr 13th 2011, 02:20 AM

NonCommAlg

Quote:

Originally Posted by student2011

Show that if is any multiplicative closed subset of where is commutative ring with unity,

if , then for some integer . so if , then . thus .
this proves that .
for the converse, let and be such that . then , for some integer . so , for some and . thus , for some . thus and hence .
therefore